PREDICTION OF ELASTIC CONSTANTS AND THERMAL EXPANSION
parametric functions that represent such effects are difficult to derive. These effects are
not represented in the codes.
Another level of idealization of unit cells is provided by codes that compute the
preform geometry by analyzing mechanical conditions during the textile forming process.
Reference [5.24] describes a code (BRAID; not included in the handbook) which
determines yarn paths based on the tensile forces applied during the textile process,
contact relations between the yarns, and the dry yarn stiffness. The yarn path and twist
are predicted in terms of spline functions. BRAID is currently restricted to considering
yarns that remain uniform in cross-section, which is not always realistic.
Finally, there are commercial solid modeling tools that may be used to create
bodies with complex geometry on a grid suitable for finite element analysis. These tools
use sophisticated Boolean operations and computer graphics to aid model generation.
Their application to textiles has been demonstrated [5.25], but the approach is not well
developed and appears too time consuming for practical use. Textile preforms involve
multiple yarns touching at many cross-over points, which makes them difficult to mesh in
such detail. Moreover, the agreement in the elastic regime of experimental data and
models based on much simpler geometrical representations implies that the extra level of
detail is unnecessary in predicting elastic constants. It may even be misleading in
analyzing local stress distributions, because of the neglect of geometrical irregularity.
All of the approaches described above assume that the unit cell geometry is
deterministic and repeatable.
Modified Laminates
Instead of using a unit cell, an alternative approach to modeling the geometry of
quasi-laminar textiles is to represent them simply as laminates of continuous,
translationally invariant plies, just like a conventional tape laminate. The geometry of the
laminate is then completely described by the thicknesses, orientations, and stacking
sequences of the layers.
